(x-2)x(x-5)=0

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Solution for (x-2)x(x-5)=0 equation: 


Simplifying
(x + -2) * x(x + -5) = 0

Reorder the terms:
(-2 + x) * x(x + -5) = 0

Reorder the terms:
(-2 + x) * x(-5 + x) = 0

Reorder the terms for easier multiplication:
x(-2 + x)(-5 + x) = 0

Multiply (-2 + x) * (-5 + x)
x(-2(-5 + x) + x(-5 + x)) = 0
x((-5 * -2 + x * -2) + x(-5 + x)) = 0
x((10 + -2x) + x(-5 + x)) = 0
x(10 + -2x + (-5 * x + x * x)) = 0
x(10 + -2x + (-5x + x2)) = 0

Combine like terms: -2x + -5x = -7x
x(10 + -7x + x2) = 0
(10 * x + -7x * x + x2 * x) = 0
(10x + -7x2 + x3) = 0

Solving
10x + -7x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -7x + x2) = 0

Factor a trinomial.
x((2 + -1x)(5 + -1x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 2, 5}

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